Mathematical Modeling Models Analysis and Applications by Sandip Banerjee
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Mathematical Modeling Models Analysis and Applications by Sandip Banerjee

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Preface to Mathematical Modeling eBook

Almost every year, a new book on mathematical modeling is published, hence the inevitable question is: Why another? The answer springs from the fact that it is rare to find a book that covers modeling with all types of differential equations in one volume.

In my study of books on mathematical modeling with differential equations, none of them covered all the aspects of differential equations.

It is this that motivated me to write a book on mathematical modeling that will cover modeling with all kinds of differential equations, namely, ordinary, partial, delay and stochastic.

The book also contains a chapter on discrete modeling, consisting of difference equations. It is this aspect of the book that makes it unique and complete and is one of its salient features.

Mathematical modeling is an important aspect of the study of science and engineering. Even social sciences involve mathematical modeling.

The primary aim of the book is to work towards creating in the reader an awareness of the concepts involved in mathematical modeling so as to build a solid foundation in the subject.

Since mathematical modeling involves a diverse range of skills and tools, I have focused on techniques that would be of particular interest to engineers, scientists and others who use models of discrete and continuous systems.

In an age when computers rule, students of engineering and science will be better placed if they understand and use the mathematics that is the basis of computers.

Mathematics is necessary for engineering and science. This will remain unaltered in spite of all changes that may come about in computation.

I never tire of telling my students that it is a risky proposition to accept computer calculations without having recourse to some parallel closed-form modeling to verify the veracity of the results.

Finally, it is fun and satisfying to do mathematical manipulations that explain how and why things happen. My target audience is undergraduates who are keen to grasp the basics of mathematical modeling.

Graduate students who want to use mathematical modeling in their research will also find the book useful.

My experience with books on mathematical modeling has been that they are effective in some areas of mathematical modeling using a particular kind of differential equation needed for the model (either ODE/PDE/DDE or even stochastic)

But never consider the complete picture as far as modeling with differential equation is concerned. It is important for students to recognize the relevance and application of their knowledge of mathematics to practical applications.

Author: Sandip Banerjee